DALHM Progress Meeting September 2003

People Mike Wiltshire Imaging Sciences Dept, Hammersmith Hospital, Jo Hajnal Imperial College London Ian Young John Pendry Department of Physics, Blackett Laboratory, Wayne Williams Imperial College London Vassilis Yannopapas David Edwards Department of Engineering Sciences, Chris Stevens University of Oxford Laszlo Solymar Katya Shamonina University of Osnabruck

Activities Quantitative measurement of field distributions transmitted through “faceplate” Reported (and augmented) MRI experiments on “faceplate” transmission at ISMRM

Very near field conditions In the very near field, for distances r << l, we can neglect retardation Then E and H are decoupled, leading to the … Electrostatic or Magnetostatic approximation E is controlled by e H is controlled by m Provides an exemplar for LHM

Swiss Roll metamaterial “faceplate” Construct 300 off, 50 mm long, Swiss Rolls Tune them all to 21.5 ± 0.1 MHz, using capacitively coupled sleeves overhanging by 10 mm Hexagonal packing to make a slab of material, 200mm diagonal, 60 mm thick This is the material. All individually tuned to the same frequency with a sleeve. Alter the number of turns in the sleeve to get the tuning. Made Steve become a Health Care Assistant in our local Hospital! Thanks to John Cobb for making the rolls and to Stephen Wiltshire for help with the tuning

Scanning Experiments Quantitative measurement of transmitted field distributions using Oxford XY table 3 mm loop as source 3 orthogonal 3 mm loop receivers Scan in xz and xy planes Sweep frequency 15 – 35 MHz Record amplitude and phase for all 3 polarisations Process as movies of Hz distribution vs frequency

Some predictions… We consider electromagnetic waves propagating through a highly anisotropic, effective medium, and solve Maxwell’s Equations The condition for solution is For mx = 1 and mz →∞, kz = ±k0, so kz is independent of kx, The input magnetic field pattern is transferred unchanged to the output face The (uniform) material behaves like “magnetic wires” or a “magnetic faceplate” The full version of this is in slides 18 – 20. We write down Maxwell’s equations for propagation through an anisotropic magnetic material. Write the characteristic equation in terms of B, and look for the conditions for solution. The eigenvalue equation is given here. When we look at the limit of mu(z) -> infinity, we find everything is independent of kx, so all values of kx are treated the same, and detail on all scales goes uniformly through the slab. Normally, kx and kz are related, and the different kx propagate differently.

The prediction for real materials…? We have a material with finite anisotropy and loss At 21.3 MHz, l ~ 14m. So in , and , i.e. the material does not transport the image perfectly Attenuation becomes significant for Im(kzd) ≈ 1, or kx(max) ≈ b / d which limits the resolution to With b ≈ 6 and d = 60 mm, D ≈ 10 mm, about the same size as the rolls For a real material, we have finite anisotropy and finite loss. On resonance, mu is pure imaginary, and ~35 K0 ~ 2pi / 14 metre; kx ~ 2pi / 14 mm, so we can ignore k0. Hence the relation between kx and kz. Putting the numbers in for the material gives a resolution comparable to the rolls dimension. Note that the resolution here is what we would find for a uniform anisotropic medium, were one to exist. This Delta is NOT due to the rolls, it just happens to be (by design) about the same size as the rolls.

21.3 MHz, m″ = 36

Further Predictions… The condition for solution was If mz →0, then kx → 0, and only the a uniform magnetic field pattern is transferred to the output face.

29.7 MHz, m′ = 0

Further Predictions… The condition for solution was Recall that k0 ~ 2p/14m whereas kx ~ 2p/14mm, so kx >> k0 For mx = +1 and mz = -1, kz = ±kx, so the magnetic field pattern travels at 45° to the output face (?)

24.75 MHz, m′ = -1

22.45 MHz

23.25 MHz

JBP Analysis for dielectric For semi-infinite slab, where

Analysis (2) Calculate transmission vs e for a given kx See “fringes” Need to take into account:- Range of kx Finite sample size

Summary Detailed measurements made of magnetic field distribution from dipole source transmitted through Swiss Roll slab Rich variety of structure observed for m < 0 Still needs full analysis: how good is effective medium model?

MRI Experiments Build & tune loop & ‘M’ antennae to 21.3 MHz Use in transmit – receive mode to excite & detect spins in “Spenco” Control experiment with “Spenco” placed on top of antenna Set RF amplitude so that only spins close to the source were excited Multi-slice spin-echo imaging Repeat experiment with Swiss Roll slab between antenna and “Spenco” Centre frequency changed by 30ppm (Ni contamination in Espanex) No change of RF amplitude required to optimise Compare to lab experiments “Spenco” Antenna Excited spins “Spenco” Antenna Excited spins Swiss Roll Slab (60 mm) So that validated our understanding of what’s going on. Now for some imaging. In the following slides, I have set the lab data alongside the MRI data: the lab data is quantitative, the MR qualitative. This slide shows the MR set up, with the control experiment & the faceplate experiment done under the same conditions. Note that we did look at the RF amplitude, to see if the optimum amplitude changed, but it didn’t. We also did measurements using the head coil as the detector: these weren’t as good as those shown here when we used the antennae as both source & receiver. All multi slice spin-echo with TE = 10, TR = 400, Flip 90, 128 X 256 matrix, 5 or 10 mm slices, FOV between 160 and 240mm

65 mm diameter single loop antenna Scanning with a 3 mm probe Source Plate (60 mm) Detector 68 mm Source Detector 8 mm MRI Images through the Swiss Roll faceplate Reference Amplitude Phase This compares the behaviour for the 65mm loop. The lab experiment was done in the same way as for slide 8, by tracking the 3mm detector loop across the surface of the material, and again at the equivalent height without the material (H-60mm). Note (a) the zero at the diameter of the 65 mm loop, with a pi phase change at the wire position, and (b) the low intensity outside the loop. The MR reference was straight into spenco with no material present. Note it’s not uniform inside the loop. The amplitude image shows not only the wire loop, but also the field within the loop, albeit at lower amplitude (but see also the lab scan which is also low inside the loop). The phase map shows that there’s a pi change at the loop itself: the inside is white, whereas there’s a black ring around the outside. Lack of signal gives indeterminate phase. So the flux does indeed go up the middle & down the outside!

Imaging Results Lab Scan MRI Scans Antenna Reference Through Swiss Rolls MRI Scans These are the M results. The antenna is 2 (anti)parallel wires that generate a line of flux. The lab scan is with a 3mm diameter loop across the surface, showing the flux being guided. Note that there is a null either side of the M where the vertical fields cancel, and this is reproduced accurately. The dynamic range of this plot is >20dB The MR scans are for the spenco on top of the M (reference), and with the material interposed. See the correspondence between the lab & MR scans. Recall that resolution is limited by both the roll size and the loss: we need smaller rolls with lower loss to do better.

Conclusion Imaging was achieved through metamaterial M pattern was transferred through slab & back to detector No lateral spreading beyond roll structure Material acts as magnetic “faceplate” Metamaterials can provide novel magnetic behaviour and functionality

Next Steps Key Questions Finish analysis of field patterns Model impact of finite sample size Is effective medium model adequate? Construct & characterise isotropic log-pile sample Metamaterial structures as flux manipulators Yoke Compressor Key Questions Negative e materials at RF? Space – filling isotropic materials with –ve index? Noise